We have imaged the disc of the young star HL Tau using the VLA at 1.3 cm, with 0.08 resolution (as small as the orbit of Jupiter). The disc is around half the stellar mass, assuming a canonical gas-mass conversion from the measured mass in large dust grains. A simulation shows that such discs are gravitationally unstable, and can fragment at radii of a few tens of AU to form planets. The VLA image shows a compact feature in the disc at 65 AU radius (confirming the `nebulosity of Welch et al. 2004), which is interpreted as a localised surface density enhancement representing a candidate proto-planet in its earliest accretion phase. If correct, this is the first image of a low-mass companion object seen together with the parent disc material out of which it is forming. The object has an inferred gas plus dust mass of approximately 14 M(Jupiter), similar to the mass of a proto-planet formed in the simulation. The disc instability may have been enhanced by a stellar flyby: the proper motion of the nearby star XZ Tau shows it could have recently passed the HL Tau disc as close as ~600 AU.